Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, interactive explorations.
Used and loved by over 6 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, interactive explorations.
Used and loved by over 6 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Problems of the Week
Contribute a problem- Week of December 17
- Week of December 10
- Week of December 3
- Week of November 26
- Week of November 19
- Week of November 12
- Week of November 5
- Week of October 29
- Week of October 22
- Week of October 15
- Week of October 8
- Week of October 1
- Week of September 24
- Week of September 17
- Week of September 10
- Week of September 3
- Week of August 27
- Week of August 20
- Week of August 13
- Week of August 6
- Week of July 30
- Week of July 23
- Week of July 16
- Week of July 9
- Week of July 2
- Week of June 25
- Week of June 18
- Week of June 11
- Week of June 4
- Week of May 28
- Week of May 21
- Week of May 14
- Week of May 7
- Week of April 30
- Week of April 23
- Week of April 16
- Week of April 9
- Week of April 2
- Week of March 26
- Week of March 19
- Week of March 12
- Week of March 5
- Week of February 26
- Week of February 19
- Week of February 12
- Week of February 5
- Week of January 29
- Week of January 22
- Week of January 15
- Week of January 8
- Week of January 1
- Week of December 25
- Week of December 18
- Week of December 11
- Week of December 4
- Week of November 27
- Week of November 20
- Week of November 13
- Week of November 6
- Week of October 30
- Week of October 23
- Week of October 16
- Week of October 9
- Week of October 2
- Week of September 25
- Week of September 18
- Week of September 11
- Week of September 4
- Week of August 28
- Week of August 21
- Week of August 14
- Week of August 7
- Week of July 31
- Week of July 24
- Week of July 17
- Week of July 10
- Week of July 3
- Week of June 26
- Week of June 19
- Week of June 12
- Week of June 5
- Week of May 29
- Week of May 22
- Week of May 15
- Week of May 8
- Week of May 1
- Week of April 24
- Week of April 17
- Week of April 10
- Week of April 3
- Week of March 27
- Week of March 20
- Week of March 13
- Week of March 6
- Week of February 27
- Week of February 20
- Week of February 13
- Week of February 6
\[ \large \begin{align} 51 \times 51 &= {\color{blue}26}{\color{red}01} \\ 52 \times 52 &= {\color{blue}27}{\color{red}04} \\ 53 \times 53 &= {\color{blue}28}{\color{red}09} \\ 54 \times 54 &= {\color{blue}29}{\color{red}16} \\ 55 \times 55 &= {\color{blue}30}{\color{red}25} \\ 56 \times 56 &= {\color{blue}31}{\color{red}36} \\ & \vdots \end{align} \]
What is the value of \( 57 \times 57?\)
Bonus: Can you explain why this pattern appears, and when it breaks?
by
Chung Kevin
Are you sure you want to view the solution?
In the diagram, the yellow and red circles are identical and are both centered on the larger circle's diameter.
Which has a larger area?
by
Chung Kevin
Are you sure you want to view the solution?
In a 90-question, multiple-choice test, a student gets
- \(+4\) for a correct answer
- \(-1\) for an incorrect attempt.
If the student attempted every single question, can he or she get a total score of exactly 300?
For example, if the student only got 60 correct answers (30 incorrect), then the total score would be \(60\times4 - 30\times1= 210. \)
by
Kalpok Guha
Are you sure you want to view the solution?
What mass (in kilograms) on the left side would keep the system in balance?
by
Ahmed Almubarak
Are you sure you want to view the solution?
We have two copper spheres of the same radius; one is hollow (vacuum inside) and the other is solid. Initially, both spheres are in a vacuum at the same temperature. Then they are heated up to the same temperature which causes them both to expand.
Which sphere has the greater final radius?
by
Pranshu Gaba
Are you sure you want to view the solution?